Thanks for the insights. I am interested in learning all this stuff. Am currently going through just Schrodinger's Equation. Do you have book recommendation(s) that include insights everywhere just like what you shared? Thanks.
replyThese are books to train physicists, accessable-ish to a math heavy engineering undergraduate degree holder. The insights above are my own and extractable from this material but not necessarily stated out loud (unless I'm unconsciously plagiarizing which is entirely possible)
reply* David Griffiths - Introduction to Elementary Particles
* Chris Quigg - Gauge Theories of the Strong, Weak, and Electromagnetic Interactions
And the wonderful Richard Behiel's videos on YouTube https://www.youtube.com/watch?v=8Iu74b5iCuQ
To add to this, this "square root" operation done to derive the Dirac equation is where spinors i.e. electron spin i.e. the Pauli exclusion principle i.e. the reason atoms exist at all comes from. Likewise antimatter. The "second order in time" of the Klein-Gordon equation comes from adding relativity and the "fix" reducing that to first order time is the source of antimatter and spin.
replySo yes very much so relativistic effects are a foundational part of QM.